Integration of and a Solution for Proof Problems and Query-Answering Problems

• Published in: Knowledge Discovery, Knowledge Engineering and Knowledge Management pp. 215 - 229
• Main Authors: Akama, Kiyoshi, Nantajeewarawat, Ekawit
• Format: Book Chapter
• Language: English
• Published: Berlin, Heidelberg Springer Berlin Heidelberg
• Series: Communications in Computer and Information Science
• Subjects: Equivalent transformation; Proof problems; Query-answering problems; Solving logical problems
• ISBN: 3662465485; 9783662465486
• ISSN: 1865-0929; 1865-0937
• DOI: 10.1007/978-3-662-46549-3_14

Proof problems have long been the main target for logical problem solving. A problem in this class is a “yes/no” problem concerning with checking whether one logical formula is a logical consequence of another logical formula. Meanwhile, the importance of anther class of problems, query-answering problems (QA problems), has been increasingly recognized. A QA problem is an “all-answers finding” problem concerning with finding all ground instances of a query atomic formula that are logical consequences of a given logical formula. Several specific subclasses of QA problems have been addressed based on solution techniques for proof problems, without success of finding general solutions. In order to establish solution methods for proof problems and QA problems, we integrate these two classes of problems by embedding proof problems into QA problems. Construction of low-cost embedding mappings from proof problems to QA problems is demonstrated. By such embedding, proof problems can be solved using a procedure for solving QA problems. A procedure for solving QA problems based on equivalent transformation is presented. The presented work provides a new framework for integration of proof problems and QA problems and a solution for them by the general principle of equivalent transformation.